The long term objective of this research is to develop new computer software that simulates the propagation of ultrasound through a specified object. Simulation software exists in a variety of engineering disciplines, for example in electromagnetics and stress-strain analysis. Ultrasound simulation is much less common. A two-dimensional ultrasound simulation software package has been available for several years. However, the lack of any 3D ultrasound simulation software has prevented a broader application of such techniques. One area which has suffered has been the use of ultrasound to assess bone, for example, to diagnose and manage osteoporosis. Three-dimensional simulation software would be expected to have a signficant positive impact on furthering understanding on how ultrasound interacts with bone, and ultimately, on developing better devices for bone fracture risk determination. The specific aim of this research is to demonstrate the feasibility of using a standard desktop computer to accurately simulate the full 3D and 3D-axisymmetric solutions to the elastic wave equation, at ultrasonic frequencies. A further specific aim is to simulate the 3D propagation of ultraound through bone. A finite difference approach will be utilized in deriving the algorithms. PROPOSED COMMERCIAL APPLICATIONS: Computer software for 3D simulation of ultrasound would have widespread use. A 2D version of the software has been sold to many commercial and academic institutions around the world. Considering the more realistic representations offered by the 3D software to be developed in this proposal, it is expected that even a broader market would be reached. Applications broader than bone and osteoporosis, such as in non-destructive testing in general, would be expected to significantly increase.